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2018 Dimension functions for spherical fibrations
Cihan Okay, Ergün Yalçin
Algebr. Geom. Topol. 18(7): 3907-3941 (2018). DOI: 10.2140/agt.2018.18.3907

Abstract

Given a spherical fibration ξ over the classifying space B G of a finite group G we define a dimension function for the m –fold fiber join of ξ , where m is some large positive integer. We show that the dimension functions satisfy the Borel–Smith conditions when m is large enough. As an application we prove that there exists no spherical fibration over the classifying space of Qd ( p ) = ( p ) 2 SL 2 ( p ) with p –effective Euler class, generalizing a result of Ünlü (2004) about group actions on finite complexes homotopy equivalent to a sphere. We have been informed that this result will also appear in upcoming work of Alejandro Adem and Jesper Grodal as a corollary of a previously announced program on homotopy group actions due to Grodal.

Citation

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Cihan Okay. Ergün Yalçin. "Dimension functions for spherical fibrations." Algebr. Geom. Topol. 18 (7) 3907 - 3941, 2018. https://doi.org/10.2140/agt.2018.18.3907

Information

Received: 30 October 2017; Revised: 1 June 2018; Accepted: 11 June 2018; Published: 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07006381
MathSciNet: MR3892235
Digital Object Identifier: 10.2140/agt.2018.18.3907

Subjects:
Primary: 55M35
Secondary: 55S10, 55S37

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 7 • 2018
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